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Bifurcation in Z2-symmetry quadratic polynomial systems with delay

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  • Zhang, Chunrui
  • Zheng, Baodong

Abstract

Z2-symmetry systems are considered. Firstly the general forms of Z2-symmetry quadratic polynomial system are given, and then a three-dimensional Z2 equivariant system is considered, which describes the relations of two predator species for a single prey species. Finally, the explicit formulas for determining the Fold and Hopf bifurcations are obtained by using the normal form theory and center manifold argument.

Suggested Citation

  • Zhang, Chunrui & Zheng, Baodong, 2009. "Bifurcation in Z2-symmetry quadratic polynomial systems with delay," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3078-3086.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:3078-3086
    DOI: 10.1016/j.chaos.2009.04.009
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    References listed on IDEAS

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    1. Yuan, Yuan, 2007. "Dynamics in a delayed-neural network," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 443-454.
    2. Peng, Mingshu & Yuan, Yuan, 2008. "Complex dynamics in discrete delayed models with D4 symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 393-408.
    3. Yu, P. & Han, M., 2007. "On limit cycles of the Liénard equation with Z2 symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 617-630.
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